Fracture and size effect on strength of plain concrete disks under biaxial flexure analyzed by microplane model M7

Kedar Kirane, Zdeněk P. Bažant, Goangseup Zi

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


The biaxial tensile strength of concrete (and ceramics) can be easily tested by flexure of unreinforced circular disks. A recent experimental study demonstrated that, similar to plain concrete beams, the flexural strength of disks suffers from a significant size effect. However, the experiments did not suffice to determine the size effect type conclusively. The purpose of this study is to use three-dimensional stochastic finite-element analysis to determine the size effect type and shed more light on the fracture behavior.Afinite-element code using the microplane constitutive Model M7 is verified and calibrated by fitting the previously measured load-deflections curves and fracture patterns of disks of thicknesses 30, 48, and 75 mm, similar in three dimensions, and on flexure tests on four-point loaded beams. It is found that the deformability of the supports and their lifting and sliding has a large effect on the simulations, especially on the fracture pattern, and the strength and Young's modulus of concrete must be treated as autocorrelated random fields. The calibrated model is then used to analyze the size effect over a much broader range of disk thicknesses ranging from 20 to 192 mm. The disks are shown to exhibit the typical energetic size effect of Type I, that is, the disks fail (under load control) as soon as the macrofracture initiates from the smooth bottom surface. The curve of nominal strength versus size has a positive curvature and its deterministic part terminates with a horizontal asymptote. The fact that material randomness had to be introduced to fit the fracture patterns confirms that the Type 1 size effect must terminate at very large sizes with a Weibull statistical asymptote, although the disks analyzed are not large enough to discern it.

Original languageEnglish
Pages (from-to)604-613
Number of pages10
JournalJournal of Engineering Mechanics
Issue number3
Publication statusPublished - 2014


  • Biaxial test
  • Concrete
  • Damage
  • Finite-element method (FEM)
  • Flexural strength
  • Fracture
  • Size effect
  • Stochastic models

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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